2008/01/23 by Mikhail Zaslavskiy, Zaslavskiy, Mikhail, Francis Bach +4 · 8 citations
Computer Science · Decision Sciences · #Advanced Image and Video Retrieval Techniques #Computer Vision and Pattern Recognition (cs.CV) #Data Quality and Management #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Graph Theory and Algorithms #cs.CV #cs.DM
paper · pdf · doi:10.48550/arxiv.0801.3654
23 pages, 13 figures,typo correction, new results in sections 4,5,6
openalex publication_date 2008/01/23 · arxiv created 2008/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four datasets: simulated graphs, QAPLib, retina vessel images and handwritten chinese characters. In all cases, the results are competitive with the state-of-the-art.